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O. M. Mulyava, M. M. Sheremeta. A remark to the growth of positive functions and its application to Dirichlet series, Mat. Stud. 44 (2015), 161–170. For a function Φ continuos on (−∞,+∞) increaing to +∞ the lower and upper estimates for α(Φ(qσ)) αp(Φ(σ)) are found, where p > 1, q > 1 and α is positive function continuous on [x0,+∞), increasing to +∞. The above results applied to Dirichlet series with positive exponents.